Non-signaling Approximations of Stochastic Team Problems

TL;DR

This paper introduces a hierarchy of non-signaling approximations for finite stochastic team problems, establishing LP methods for near-optimal policies and highlighting open questions in quantum policy optimization.

Contribution

It develops a hierarchy of decision rules, proves approximation bounds for non-signaling policies, and formulates LP methods for sequential teams, advancing the understanding of non-classical policy classes.

Findings

Small distance between extendible non-signaling and decentralized policies

LP approximation for sequential teams established

Open problem on quantum-correlated policy optimization

Abstract

In this paper, we consider non-signaling approximation of finite stochastic teams. We first introduce a hierarchy of team decision rules that can be classified in an increasing order as randomized policies, quantum-correlated policies, and non-signaling policies. Then, we establish an approximation of team-optimal policies for sequential teams via extendible non-signaling policies. We prove that the distance between extendible non-signaling policies and decentralized policies is small if the extension is sufficiently large. Using this result, we establish a linear programming (LP) approximation of sequential teams. Finally, we state an open problem regarding computation of optimal value of quantum-correlated policies.